First-principles calculations are used to establish that the electronic structure of graphene ribbons with zigzag edges is unstable with respect to magnetic polarization of the edge states. The magnetic interaction between edge states is found to be remarkably long ranged and intimately connected to the electronic structure of the ribbon. Various treatments of electronic exchange and correlation are used to examine the sensitivity of this result to details of the electron-electron interactions, and the qualitative features are found to be independent of the details of the approximation. The possibility of other stablization mechanisms, such as charge ordering and a Peierls distortion, are explicitly considered and found to be unfavorable for ribbons of reasonable width. These results have direct implications for the control of the spin-dependent conductance in graphitic nanoribbons using suitably modulated magnetic fields.

Graphene has remarkable electronic properties, such as ballistic transport and quantum Hall effects, and has also been used as a support for samples in high-resolution transmission electron microscopy and as a transparent electrode in photovoltaic devices. There is now a demand for techniques that can manipulate the structural and physical properties of graphene, in conjunction with the facility to monitor the changes in situ with atomic precision. Here, we show that irradiation with an 80 kV electron beam can selectively remove monolayers in few-layer graphene sheets by means of electron-beam-induced sputtering. Aberration-corrected, low-voltage, high-resolution transmission electron microscopy with sub-ångström resolution is used to examine the structural reconstruction occurring at the single atomic level. We find preferential termination for graphene layers along the zigzag orientation for large hole sizes. The temporal resolution can also be reduced to 80 ms, enabling real-time observation of the reconstruction of carbon atoms during the sputtering process. We also report electron-beam-induced rapid displacement of monolayers, fast elastic distortions and flexible bending at the edges of graphene sheets. These results reveal how energy transfer from the electron beam to few-layer graphene sheets leads to unique structural transformations.

Focused electron beam irradiation has been used to create mono and divacancies in graphene within a defined area, which then act as trap sites for mobile Fe atoms initially resident on the graphene surface. Aberration-corrected transmission electron microscopy at 80 kV has been used to study the real time dynamics of Fe atoms filling the vacancy sites in graphene with atomic resolution. We find that the incorporation of a dopant atom results in pronounced displacements of the surrounding carbon atoms of up to 0.5 Å, which is in good agreement with density functional theory calculations. Once incorporated into the graphene lattice, Fe atoms can transition to adjacent lattice positions and reversibly switch their bonding between four and three nearest neighbors. The C atoms adjacent to the Fe atoms are found to be more susceptible to Stone-Wales type bond rotations with these bond rotations associated with changes in the dopant bonding configuration. These results demonstrate the use of controlled electron beam irradiation to incorporate dopants into the graphene lattice with nanoscale spatial control.

Theoretical calculations, based on hybrid exchange density functional theory, are used to show that in graphene a periodic array of defects generates a ferromagnetic ground state at room temperature for unexpectedly large defect separations. This is demonstrated for defects that consist of a carbon vacancy in which two of the dangling bonds are saturated with H atoms. The magnetic coupling mechanism is analysed and found to be due to an instability in the π electron system with respect to a long-range spin polarisation characterised by alternation in the spin direction between adjacent carbon atoms. The disruption of the π-bonding opens a semiconducting gap at the Fermi edge. The size of the energy gap and the magnetic coupling strength are strong functions of the defect separation and can thus be controlled by varying the defect concentration. The position of the semiconducting energy gap and the electron effective mass are strongly spin-dependent and this is expected to result in a spin asymmetry in the transport properties of the system. A defective graphene sheet is therefore a very promising material with an in-built mechanism for tailoring the properties of the spintronic devices of the future.

Two distinct configurations of the monovacancy in graphene have been observed using aberration-corrected transmission electron microscopy (AC-TEM) at 80 kV. The predicted lower energy asymmetric monovacancy (MV), exhibiting a Jahn-Teller reconstruction (r-MV), has been observed, but in addition, we have imaged instances of a symmetric monovacancy (s-MV). We have used geometric phase analysis (GPA) to quantitatively determine the strain in the lattice surrounding these two defect configurations and show that the Jahn-Teller reconstruction generates significant extra strain compared to the symmetric MV case. Density functional theory calculations demonstrate that our experimental images of the two different monovacancies show good agreement with both the low energy r-MV and the metastable structures.